If there were any doubt about the value of the Hapgood Theatre Company, the proof took center stage in the troupe’s latest production, which opened March 12 at the Nick Rodriguez Community Center theater.

With the stunning Sarah Kate Anderson as the protagonist and talented Josy Miller at the directorial helm, David Auburn’s “Proof” was both elegant and enticing, delighting audiences from start to finish. The Pulitzer Prize-winning script, which was infused with incisive dialogue and a well-told plot, came to life here with captivating characters, who asked — and answered — profound questions about love, insanity and loss, and did so with a surprising amount of humor.

The four-character drama centers on the twentysomething Catherine, who has given up her life to care for her father, a mathematical genius who is now mentally ill.

After he dies of a heart attack, she is beside herself, insecure and confused, torn about what to do. That is until a former student of her father’s comes to wade through his work in an attempt to find any long-lost mathematical proof. The eager postgraduate student winds up engaged in a relationship with Catherine. But is he really in love with her or is he just trying to steal her father’s work? And where’s the proof about who actually wrote the important mathematical papers?

Anderson, a Santa Cruz-based actor, was perfectly cast as Catherine, the brilliant but prone-to-depression daughter. With long, curly, frazzled red hair and slightly disheveled clothing, she looks every bit the part of a torn young woman who’s put her education and life on hold to care for her once-brilliant father.

Anderson infuses the character with just the right amount of fragility and toughness, easily displaying her wit, trading barbs with the best of them, using her body movements and facial expressions to indicate her lethargy, her anger, her eagerness. On the stage nearly all of the play, Anderson is a genius at engrossing the audience, believably metamorphosing from her cocoon of insecurity into an assured, attractive young woman and a force to be reckoned with. She also has one of the best Act 1 ending lines you’ll ever hear — but to reveal it would ruin the surprise.

Equity actor Dan Cawthon of Walnut Creek plays her father, Robert, the beloved math teacher who made breakthroughs early on but whose later life was marked by delusion and mental illness. Cawthon is on stage only in the flashbacks but does a fine job balancing the roles of loving dad and unstable former genius. He offers a nice blend of humor, sympathy and pain.

Playing his former student Hal Dobbs is Kyle Payne of San Leandro. Payne does a good job portraying the postgraduate mathematician, who believes that “a great mind does not just shut down,” and is intent of finding the “gold” in Robert’s notebooks. Payne is every bit the nerdy but likable and somewhat shy math teacher who lacks the brilliance of his mentor or his girlfriend.

Rounding out the cast is Kim Saunders of Mountain View as Claire, Catherine’s older sister, a career woman who thinks she knows best about everything from what her sister should take in her coffee to where she should live. Saunders plays the role with aplomb, being every bit the overbearing older sister, showing little interest in her father’s funeral, little understanding of her sister’s wants and needs while still trying to protect her from the horrible fate of her father.

Set in modern-day Chicago, the show takes place against the backdrop of a well-designed, detailed red brick back porch setting. Designed by Sean O’Skea, it faithfully recreates an older South Side Chicago home with doors and windows offering a glimpse inside to the living spaces and book-lined walls.

Between scenes, a woman’s beautiful haunting songs set the tone for this suspense-filled, gripping drama.

Though the key plot device is a complex math formula, you needn’t know anything about numbers to enjoy this play. With fast-paced dialogue, top-notch acting and directing and a well-told story, Hapgood’s “Proof” has just the right formula to win over audiences.

Judith Prieve is an East Bay journalist. A graduate of the University of Wisconsin-Madison, she has worked as a reporter, features editor and assistant metro editor at newspapers in Wisconsin and Northern California and has been at what is now the Bay Area News Group for more than 25 years.